A Fenchel Duality Aspect of Iterative I-Projection Procedures |
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| Authors: | Bhaskar Bhattacharya Richard L. Dykstra |
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| Affiliation: | (1) Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, U.S.A.;(2) Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA, 52242, U.S.A. |
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| Abstract: | In this paper we interpret Dykstra's iterative procedure for finding anI-projection onto the intersection of closed, convex sets in terms of itsFenchel dual. Seen in terms of its dual formulation, Dykstra's algorithm isintuitive and can be shown to converge monotonically to the correctsolution. Moreover, we show that it is possible to sharply bound thelocation of the constrained optimal solution. |
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| Keywords: | Algorithm convex sets Fenchel duality I-projections iterative Kullback-Leibler |
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